Regular factors in graphs
type: CreativeWork
description: The first part of this dissertation deals with the influence of different parameters on the existence of a regular factor in a regular graph. Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the graph are known, besides the order and the degree of the graph. The second part deals with the question how large the edge-set of a graph can be if the graph has a unique regular factor. The focus will be on extremal bipartite graphs with a unique regular factor. An analysis of the structure shows that all extremal bipartite graphs with a unique k-factor have exactly 2k vertices of minimum degree. This result allows for positive answers on the maximal number of edges in an extremal graph if k is small. This dissertation closes with results on extremal graphs with a unique [1,k]-factor.
abstract: The first part of this dissertation deals with the influence of different parameters on the existence of a regular factor in a regular graph. Sharp sufficient conditions for the existence of a regular factor are presented, if either the radius, the chromatic number or the vertex-connectivity of the graph are known, besides the order and the degree of the graph. The second part deals with the question how large the edge-set of a graph can be if the graph has a unique regular factor. The focus will be on extremal bipartite graphs with a unique regular factor. An analysis of the structure shows that all extremal bipartite graphs with a unique k-factor have exactly 2k vertices of minimum degree. This result allows for positive answers on the maximal number of edges in an extremal graph if k is small. This dissertation closes with results on extremal graphs with a unique [1,k]-factor.
author: Hoffmann, Arne
language: eng
keywords: info:eu-repo/classification/ddc/510, Mathematik
date published: 2002
date modified: 2026-07-30T19:42:01Z
provider: RWTH Aachen University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Publikationsserver der RWTH Aachen University